67.1.36 problem 2.6 (b iii)

Internal problem ID [16301]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.6 (b iii)
Date solved : Thursday, October 02, 2025 at 10:45:31 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=3 \sqrt {x +3} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.036 (sec). Leaf size: 17

ode:=diff(y(x),x) = 3*(x+3)^(1/2); 
ic:=[y(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -16+\left (2 x +6\right ) \sqrt {x +3} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 16

ode=D[y[x],x]==3*Sqrt[x+3]; 
ic={y[1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 \left ((x+3)^{3/2}-8\right ) \end{align*}

✓ Sympy. Time used: 0.078 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*sqrt(x + 3) + Derivative(y(x), x),0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 2 \left (x + 3\right )^{\frac {3}{2}} - 16 \]